Essays in Behavioral Economics

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Essays in Behavioral Economics

Inaugural-Dissertation

zur Erlangung des Grades eines Doktors der Wirtschafts- und Gesellschaftswissenschaften

durch die

Rechts- und Staatswissenschaftliche Fakultät der Rheinischen Friedrich-Wilhelms-Universität

Bonn

vorgelegt von Florian Zimmermann

aus Leonberg

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Dekan: Prof. Dr. Klaus Sandmann Erstreferent: Prof. Dr. Armin Falk Zweitreferent: Prof. Dr. Sebastian Kube

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Acknowledgments

I thank Armin Falk for great help, advice and encouragement through all stages of my dissertation. I am still amazed by, and very grateful for the amount of time and energy he was willing to invest in my own and our joint research. His way of doing research has been very inspiring.

I also thank Paul Heidhues, Sebastian Kube and Daniel Krähmer for the help and advice. Uri Gneezy has been a wonderful host during my stays at UC San Diego. I enjoyed a lot and benefited from many discussions with him. I also thank my coauthor Mara Ewers for a great collaboration.

Bonn Graduate School of Economics has been a wonderful place to study and do research, and I thank all people who help running and improving BGSE, especially Urs Schweizer, Silke Kinzig and Pamela Mertens.

The institute in empirical economics has always been a great place to hang out and I am thankful for all the great people I was allowed to meet there over the years. Special thanks are owed to Konstanze Albrecht, Steffen Altmann, Mirko Seithe, Hannah Schildberg-Hoerisch and Matthias Wibral.

Finally and most importantly, I thank my family! My parents and my sister for their love, encouragement and support.

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List of Figures

1.1 Illustration of experimental design. . . 11

1.2 Relative frequency of choices (clumped or piecewise information) for treat-ments 1 and 2. . . 16

1.3 Relative frequency of willingness to pay for lottery for treatment 3 (clumped information) and treatment 4 (piecewise information). . . 18

2.1 Percentage of “better than average” reports for high, low and close to av-erage quiz performance, for subjects in the audience treatment and the private treatment. . . 38

2.2 Percentage of “better than average” reports for high, low and close to aver-age quiz performance subjects in feedback treatment and private treatment. 42

3.1 Summary of Treatments for Experiment 1. . . 55

3.2 Probability of being selected by principal (in the principal treatment) de-pendent on the absolute difference between two estimates. . . 61

3.3 Scatterplots of first and second estimates for principal-agent and agent treatment. . . 62

3.4 Relative frequency of deviations between estimates for principal-agent and agent treatment. . . 63

3.5 Timing of the experiment . . . 65

3.6 Relative frequency of absolute deviations from the public signal (2615) for both treatments. . . 67

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3.8 Relative frequencies of statement “Yes” for question on punishment of mur-derer for manipulation and control treatment plus relative frequency of statement “Yes” for question on second chance in life (only manipulation treatment). . . 73

3.9 Reported and actual dice roll for manipulation and control treatment. . . . 74

5.1 All information on Tuesday . . . 105

5.2 Information step by step . . . 105

5.3 Picture of bowl with peas: This bowl was shown to subjects in the estima-tion task of experiment 2. . . 114

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List of Tables

2.1 Design of the experiment . . . 34

2.2 Determinants of stated self-assessment . . . 36

2.3 Subjects’ beliefs about the other participants’ self-assessments . . . 40

2.4 Determinants of stated self-assessment in the private and feedback treatment 41

3.1 OLS, regressing subjective well-being on a constant, a treatment dummy (=1 if manipulation treatment) and several controls (health condition, sat-isfaction with field of study, optimism to find a good job in the future and number of friends). . . 76

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Introduction

Answers to virtually all questions of economic relevance require an understanding of how economic agents behave. The economic consequences of tax cuts can only be studied with a theory of how individuals, e.g., consumers, employees, employers, respond to the tax cuts. Likewise, effects of changing unemployment benefits cannot be understood without having an idea of how the unemployed, but also the employed and firms will respond to the changes. The traditional economic approach to decision-making has been to assume rational agents that possess well-defined preferences and, given beliefs that are formed through Bayesian updating and include all available information, select their preferred alternative. This approach has been very successful and provided a tractable and parsimonious workhorse to study economic behavior.

In the past decades, however, economists have started to incorporate insights from re-lated disciplines, e.g., psychology, sociology, to develop a more precise and realistic model of economic behavior. Pathbreaking studies have been (just to name a few) Kahneman and Tversky (1979), who provide a model of expected utility that incorporates loss aver-sion as well as non-bayesian belief formation, Laibson (1997), formalizing the notion of hyperbolic discounting and Rabin (1993), proposing a way to include social preferences into game-theoretic analysis. This approach has helped to align empirical phenomena that are hard to reconcile with “standard” economic assumptions. It has also lead to the development of novel policy instruments that (for example) take into account cognitive limitations and misperceptions of agents. Examples are Thaler and Benartzi (2004) for savings behavior or Hastings and Weinstein (2008) on parents’ school choice.

In the following chapters, both theory and controlled experiments are used to better understand the foundations of economic decision-making, and to derive novel economic implications. While the topics of the four chapters are rather diverse, the common theme is the attempt to contribute to a more realistic model of economic behavior. In chapter

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1, we conduct a controlled lab experiment to test a key implication of a recent model developed in Kőszegi and Rabin (2009). Chapters 2 and 3 are similar in structure. Both propose simple behavioral models whose central implications are then tested experimen-tally. Chapter 4 uses insights from chapter 3 as well as from a related literature in psychology to provide an explanation for so-called anchoring effects, a phenomenon that is at odds with traditional models of economic decision-making. In the following, the four chapters of this dissertation are briefly summarized.

Chapter 1 focuses on individuals’ attitudes towards the timing of information. We test a theoretical prediction by Kőszegi and Rabin (2009), that people prefer to get information “clumped together” rather than piecewise. We conduct a controlled lab experiment where subjects participate in a lottery and can choose between different resolutions of uncertainty (clumped or piecewise). In two treatments we analyze which kind of resolution is preferred. Two additional treatments allow us to get a quantitative measure of subjects’ preferences over different information structures. Our data does not support the prediction that piecewise information is utility-decreasing.

In chapter 2, we ask if reports of private information about skills, abilities or achieve-ments are affected by image concerns. We develop a simple model that illustrates how image utility can lead to misreporting of private information in contexts where truthful reports maximize monetary outcomes. In addition, we test the model’s predictions in a controlled lab experiment. In the experiment, all subjects go through a series of quiz questions and subsequently report a performance measure. We vary if reports are made to an audience or not and find evidence for image effects. In the audience treatment, stated reports are significantly higher than in the private treatment. This suggests that overconfident appearance might be a consequence of social approval seeking. We also find that men state higher self-assessments than women. This gender difference seems to be driven by men responding more strongly to the presence of an audience.

Chapter 3 studies the role of consistency as a signaling device. We propose a two-period model that highlights the informativeness of consistency as a signal of skills and allows to analyze consequences for behavior. In a simple principal-agent experiment we test the basic intuition of the model, that consistency is valued by others, inducing people to act consistently. In the second part of the chapter we study the consequence of early commitment for behavior. In the context of an estimation task we demonstrate that

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commitment leads to a neglect of valuable information. Furthermore, the potential of consistency as a device of social influence is studied in the context of surveys.

In Chapter 4, we provide an explanation for so-called anchoring effects. Random an-chors have been shown to systematically affect judgments and valuations. This has called into question the rationality of judgments as well as the existence of stable preference re-lations. Instead this evidence suggests that both judgments and valuations are to a large degree arbitrary. This chapter is an attempt to reconcile evidence from anchoring manip-ulations with a model where decision-makers are rational and have stable preferences or judgments.

A final remark concerning the use of the first person plural throughout this disserta-tion: it is owed to the fact that chapter 2 was developed in a collaboration with Mara Ewers, and chapters 3 and 4 are the product of joint work with Armin Falk. For reasons of consistency, the plural is also used in this introduction and chapter 1.1 _{The next four}

chapters are each presented as self-contained units.

1_{See chapter 3 for both theoretical and empirical evidence for the informativeness of consistency as a}

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Chapter 1

Clumped or Piecewise? - Evidence on

Preferences for Information

1.1

Introduction

The selection and processing of information is a key element in virtually all areas of eco-nomic decision-making. Individuals facing ecoeco-nomic choices, e.g., investing in education, choosing an optimal health insurance plan, buying a house or deciding how much to save for the future, need to choose sources of potentially helpful information and process this information to be able to make an informed decision. Likewise, economic choices affect the kind, structure and timing of information decision-makers will receive. A decision to participate in a risky enterprise implies, that the decision-maker will receive news about the success or failure of the enterprise in the future. Therefore, attitudes or preferences towards information structures can be an important factor influencing choices and behav-ior.

Furthermore, the structuring of information can serve as a policy or managerial instru-ment. Policy-makers, when providing information on, e.g, the current state of political reform or consequences from a natural disaster, need to take the impact of the timing of information provision into account. Likewise, employers providing feedback to their employees can structure the feedback to their own advantage. The traditional economic approach to decision-making, however, neglects that the information an individual receives might have direct utility consequences.

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towards information into models of decision-making.1 A key prediction of Kőszegi and Rabin (2009) is that individuals are averse to piecewise information. Thus, they should prefer to receive information in one piece rather than piece by piece.2 _{Their model provides}

explanations for various phenomena such as loss aversion over wealth, overconsumption or precautionary savings. Empirically, however, little is known about preferences for clumped or piecewise information. In this chapter, we use a controlled lab experiment to test the implication that people have a preference for information in one piece. As a whole, we find no support for this prediction.

Kőszegi and Rabin (2009) develop a dynamic model of reference-dependent preferences. A central assumption of the model is that utility depends on anticipated changes in beliefs about current and future consumption. Beliefs are rational and people are loss averse with regard to changes in their beliefs.3 _{Thus bad news decrease utility more than good news}

increase it. Furthermore it is assumed that people care less about changes in beliefs, the further away the time of belief change lies from the actual point of consumption. In other words, a person is assumed to be less sensitive to changes in beliefs, the more time lies in between news and the time of consumption. The model gives rise to informational preferences, i.e., preferences towards the timing of non-instrumental information. Loss aversion in belief changes leads to a preference for clumped information. Since bad news decrease utility more than good news increase it, decision-makers are averse to fluctuations in their beliefs. Consequently piecewise information is utility-decreasing.

In this chapter we test the prediction that piecewise information is utility-decreasing. In the experiment, subjects can choose how they want to be informed about the outcome of a lottery. They have two options: Either they learn the outcome of the lottery in

1_{Caplin and Leahy (2001) incorporate anticipatory emotions towards uncertainty resolution into an}

expected utility framework and analyze consequences, for example on portfolio choice. In another paper, Caplin and Leahy (2004), use an expected utility framework with anticipatory emotions to analyze how much information an expert should transmit to a poorly informed person.

2_{Similar implications are derived in theoretical work by Palacios-Huerta (1999) and Dillenberger}

(2010). Palacios-Huerta (1999) develops an argument why people might prefer clumped information based on an example of the model of disappointment aversion by Gul (1991). Dillenberger (2010) consid-ers a general class of recursive, non-expected preferences over compound lotteries. He shows equivalence between a preference for information in one piece and the so-called “certainty effect” by Kahneman and Tversky (1979). A related intuition can also be found in Kőszegi and Rabin (2009).

3_{The idea that reference points are determined by rational expectations has been developed in Kőszegi}

and Rabin (2006, 2007). Similar approaches can be found in the disappointment aversion models of Bell (1985), Loomes and Sugden (1986), and Gul (1991). Several recent empirical studies provide support for expectation-based reference points. See for example Abeler et al. (2011), Crawford and Meng (2011), Gill and Prowse (forthcoming) and Ericson and Fuster (forthcoming).

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one piece, or they are sequentially informed about it. Information in this setting is non-instrumental since the lottery is an exogenous event which cannot be influenced by the subjects. Subjects’ choices allow us to analyze which information structure is preferred. Two additional treatments allow us to specify a willingness to pay, i.e., a quantitative measure. In these treatments, subjects cannot choose between clumped or piecewise in-formation but are exposed to either one of the two. A subject’s choice in these treatments is to state a willingness to pay for participating in the lottery. Comparison of the aver-age willingness to pay between the two treatments provides a quantitative measure for preferences over different information structures.

Summarizing our results, we find no evidence that subjects are averse to piecewise information. When subjects can directly choose between the two information conditions, only slightly more than 50 percent prefer to receive information in one piece. This is only compatible with a preference for clumped information if one is willing to allow for very high error rates. The average willingness to pay for the lottery is more than 2 Euro higher when subjects are sequentially informed about the outcome of the lottery. We can reject the null hypothesis that subjects’ willingness to pay for the lottery is higher in the clumped information condition.

Our study is the first to provide a direct experimental test of whether individuals are averse to piecewise information. Moreover, our findings are important, as the assump-tions that lead to the prediction we test have several implicaassump-tions for behavior. Kőszegi and Rabin (2009) show that loss aversion in belief changes provides a foundation for loss aversion over total wealth as is assumed for example in prospect theory (Kahneman and Tversky (1979)). The intuition is simple. Wealth gains and wealth losses are news about current and future consumption. Consequently, loss aversion over consumption news in-duces gain-loss utility over wealth. In a two-period application, Kőszegi and Rabin (2009) show how their model can generate a novel type of overconsumption. For example, in contexts where wealth is deterministic, people might deviate from ex-ante optimal con-sumption plans and overconsume relative to the plan, because good news about increased consumption now might outweigh bad news about future consumption due to decreasing sensitivity towards belief changes. Consequently the ex-ante optimal plan is not credible. Actual consumption in period 1 will be above the ex-ante optimal level to account for the lack of credibility of the ex-ante optimal plan. Loss aversion in belief changes also gener-ates a new type of precautionary savings motive. In their two-period application, Kőszegi

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and Rabin (2009) analyze how decision-makers respond to future wealth uncertainty (re-solved in period 2). They show that decision makers respond to higher uncertainty by reducing consumption in period 1. Intuitively, future wealth uncertainty exposes decision makers to (potentially) negative belief shocks which are felt heavily due to loss aversion, but can be dampened by higher savings in period 1.

In addition, our results contribute to the experimental literature on myopic loss aver-sion (see Benartzi and Thaler (1995) and Gneezy and Potters (1997)). Gneezy and Potters (1997) let subjects repeatedly go through risky investment choices and vary the frequency with which they received feedback regarding the outcome and with which they could make their choices. They find that investments in the risky asset are higher when the frequency of feedback and choices is low. Haigh and List (2005) replicate this result with professional traders. One question that arises is whether these results are due to the frequency of choices or the frequency of feedback. Our results suggest that myopic loss aversion is most likely not driven by a direct preference for a clumped timing structure in the resolution of risk. Note that Bellemare et al. (2005) provide evidence in the oppo-site direction. They conduct an experiment similar to Gneezy and Potters (1997), with the additional twist that it allows to disentangle effects of frequency of feedback from frequency of choices. They find that manipulating feedback is sufficient to generate my-opic loss aversion. This finding is compatible with a preference for clumped information. Langer and Weber (2008), however, document the opposite. They identify frequency of choices as the relevant factor that drives myopic loss aversion.4

There exists a small empirical literature on informational preferences, but no incen-tivized study addresses the question if subjects prefer clumped information over piecewise information. Chew and Ho (1994) and Ahlbrecht and Weber (1996) are early examples. Both use questionnaire formats to examine preferences for different resolutions of uncer-tainty. More recently several incentivized experiments were conducted. Eliaz and Schotter (2007) find that subjects are willing to pay for earlier reception of non-instrumental in-formation. Eliaz and Schotter (2010) show evidence for a demand for non-instrumental information about the likelihood that a risky choice was optimal. Van Winden et al. (2011) examine how investment decisions are affected by a delay in the resolution of risk. They find a significant impact of the delay of non-instrumental information and show that

4_{Fellner and Sutter (2009) find that both factors (frequency of feedback and frequency of choices) are}

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emotions play a central role in explaining their results. Kocher et al. (2009) find that subjects holding a lottery ticket have a preference for delayed resolution of risk and that this preference is driven by positive anticipatory emotions.

The remainder of the chapter is organized as follows. The next section describes the experimental design and states hypotheses. Section 1.3 shows results and section 1.4 concludes.

1.2

Experimental Design and Hypotheses

An environment where preferences towards the timing of information can be studied needs the following features:

1. Non-instrumentality of information: information needs to be on a predetermined event that can not be affected by subjects. For this kind of information, “standard” expected utility theory predicts indifference towards the timing of information.

2. Meaningful time delays: Kőszegi and Rabin (2009) characterize differences in the timing of information by signals arriving in different time periods, leaving open the length of a time period. In principle time periods could be seconds, minutes, days or months. When testing their predictions we need to create an environment where the variation in the timing structure involves different time periods in the sense of Kőszegi and Rabin (2009). In particular very small variations might be problematic. Say for example that we would vary the timing structure by having signals arrive every 10 seconds. Then it could well be that subjects integrate signals that follow each other that closely into one signal, thereby perceiving piecewise as clumped information. Note however that while leaving the length of a time period open, Kőszegi and Rabin (2009) also do not exclude any specifications.

3. Absorption of information: to implement different timing structures, we need to make sure that subjects absorb information at the moment they receive it. If sub-jects have the possibility to delay absorption, for example by not reading information provided on a computer screen or a sheet of paper, we loose control over the timing structure.

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1.2.1

Experimental Design

We designed an experiment that captures all features discussed above. We studied four treatments in total. Intreatments 1and 2, subjects were endowed with a lottery ticket. A central characteristic of the lottery was that it contained a natural sequence of three signals about the outcome of the lottery. Each of the three signals served as a piece of information. Since the lottery outcome could not be affected by subjects, information was non-instrumental. Subjects’ choices were about how they wanted to be informed about the outcome of the lottery. We offered two possibilities: information in one piece or sequential information. Given our goal to make variations in the resolution of uncertainty meaningful we decided to run the experiment over days. The information conditions and the different steps of the experiment are illustrated in Figure 1.1. If subjects preferred to receive information clumped, the three signals were collapsed into one. Subjects were informed in one piece about the final outcome of the lottery on day 2 of the experiment. If subjects chose to receive information piecewise, they were sequentially provided with the three pieces of information. They learned the first piece on the second day of the experiment. One day after they received the second signal. On day 4 they learned the third and final piece of information regarding the lottery outcome.5 _{In order to make}

sure that subjects absorbed information by the time we revealed it, we informed them via phone calls. Via telephone we achieved full control on the timing of resolution of uncertainty about the lottery outcome.6

The only difference between treatments 1 and 2 was the lottery. Intreatment 1, part of the lottery was a starting endowment of 30 Euro (one Euro was worth 1.45 US-Dollar at the time). A fair dice was thrown three times and the numbers thrown were added up. If the total sum after three throws was larger than or equal to 13, subjects won 50 Euro which were added to their starting endowment of 30 Euro. In case the total sum was smaller than 13, subjects lost 15 Euro which were deducted from their starting capital. The lottery has an expected value of about 32 Euro and a standard deviation of 28.5. Each of the three dice throws represented a piece of information, allowing subjects to

5_{Note that in the clumped condition signals are collapsed into 1 signal that is received at day 2. Thus}

when comparing the clumped and the piecewise condition, no signals were delayed through clumping. This is important, because in Kőszegi and Rabin (2009) people only strictly prefer clumped to piecewise information if the clumped condition does not involve any delay of signals, see section 1.2.3 and Appendix A.

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update their beliefs regarding the outcome of the lottery.

Intreatment 2, we changed the payoff structure of the lottery. In Kőszegi and Rabin (2009), people are loss averse with respect to anticipated belief changes. We suspected that anticipation effects might be more pronounced the more meaningful the outcome is to subjects. While in treatment 1 stakes and the payoff difference between winning and losing were already high, we decided to use a lottery in treatment 2 which has an almost 10-times higher payoff difference. Subjects could either gain 500 Euro or zero.7 _{The lottery}

worked as follows. In three rounds three dice were thrown simultaneously. Subjects won if in at least one round, all three dice showed a six. The lottery has an expected value of about 7 Euro, and a standard deviation of roughly 58.7. As in treatment 1 each of the three rounds of dice rolls represented a piece of information.

Subjects’ choices between clumped or piecewise information in treatments 1 and 2 allow us to qualitatively examine on an individual level which information structure is preferred. Treatments 3and4allow us to specify a willingness to pay, i.e., a quantitative measure.8 _{In these treatments, subjects could not choose between the two information}

Monday Tuesday Wednesday Thursday Friday

(BonnEconLab) (Phonecall) (Phonecall) (Phonecall) (Experimenter’s Office) - Main Decision Treatment 1: clumped vs. piecewise Treatment 2: clumped vs. piecewise Treatment 3: willingness

to pay for lottery

Treatment 4: willingness

to pay for lottery - Measure for Loss Aversion

- Measure for Risk Aversion (only treatments 3 & 4) Clumped Condition: - Information about outcome of lottery Piecewise Condition: - First piece of information about outcome of lottery (result of first dice roll) Clumped Condition: - No further information about lottery Piecewise Condition: - Second piece of information about outcome of lottery (result of second dice roll) Clumped Condition: - No further information about lottery Piecewise Condition: - Third and final piece of information about outcome of lottery (result of third dice roll) Payment

Figure 1.1: Illustration of experimental design.

conditions. Instead they found themselves in one of the two conditions and were asked to

7_{In addition, in treatment 2 subjects received a show-up fee of 15 Euro.}

8_{Note that treatments 3 and 4 were conducted before treatments 1 and 2. While we do not think that}

this changes the interpretation or validity of our results in any way, we report this here for the sake of completeness and to avoid any misunderstandings.

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state their willingness to pay to participate in the lottery. The information conditions were identical to treatments 1 and 2. Subjects in treatment 3 received information clumped, subjects in treatment 4 received information piecewise. The lottery was the same as in treatment 1.

The only decision subjects had to make was to choose their willingness to pay for the lottery. We used a multiple price list format to elicit certainty equivalents.9 In particular, subjects had to make 25 choices between the lottery and a certain amount which was increased from 13 Euro to 37 Euro in increments of 1 Euro. One of the 25 choices was afterwards randomly selected and implemented. If subjects behaved consistently, they (at maximum) switched once between the lottery and the fixed payment. This switching point was used as subjects’ willingness to pay for the lottery. Comparison of the average willingness to pay for the lottery between the treatments 3 and 4 allows us to analyze if and to what degree subjects preferred clumped over piecewise information.

1.2.2

Procedural Details

In all four treatments the experiment went over 5 days, starting on a Monday and ending on Friday of the same week. On Monday subjects met in the experimental lab. They were welcomed and assigned into cabins. Then instructions were passed and read aloud.10

Subjects were instructed in detail about the lottery and the information conditions. In treatments 1 and 2, subjects were informed about both information conditions, in treat-ments 3 and 4 they were only informed about the information condition of the respective treatment. Then subjects had to make their choice. In treatments 1 and 2 they decided which information condition they preferred. In treatments 3 and 4 they stated their willingness to pay for the lottery.

In all treatments we also elicited a measure of loss aversion, following the procedure of Fehr and Goette (2007). Subjects faced two lottery choices. In choice 1 they had to decide whether they want to participate in a lottery where they could win 3 Euro with probability 1₂ or loose 2 Euro with probability 1₂. In choice 2 they had to decide if they want to participate in a lottery that consisted of four independent repetitions of the lottery in choice 1. Subjects were told that in the end of the experiment one of the two

9_{See Holt and Laury (2002) for the multiple price list format.} 10_{Instructions are provided in Appendix A.}

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choices was randomly selected and implemented. In treatments 3 and 4 we also elicited a risk measure. Subjects faced 25 choices between a lottery and a fixed payment. The lottery was the same across choices and paid zero or 3 Euro, each with probability 0.5. The fixed amount was increased in 10 Cent increments, starting from 30 Cent and going up to 270 Cent. Again, one choice was randomly picked and implemented (see Dohmen et al. (2011)).

Note that our central measures of interest (choice between clumped and piecewise information in treatments 1 and 2 and willingness to pay for the lottery in treatments 3 and 4) were all elicited on the first day of the experiment, i.e., on Monday. When subjects left the laboratory, they received a letter which reminded them of their duties for the next days, i.e., when to call the experimenter and when to pick up the money. After all subjects had left the lab on Monday, the experimenter conducted the dice rolls. From Tuesday to Thursday subjects had to call the experimenter once a day.11 _{Subjects were told that}

failing to call would lead to the loss of all their earnings from the experiment.12 During the phone calls, subjects received information about the outcome of the lottery. In the clumped information condition, subjects were informed on Tuesday whether they won in the lottery or not and which numbers were thrown for them. In the piecewise condition, subjects received one piece of information each day. Thus they usually did not know before Thursday whether they won in the lottery or not. Note that in both conditions subjects had to call once a day from Tuesday to Thursday and that the duration of the phone calls always was approximately one minute. This was made clear to subjects in the instructions. On Friday subjects had to come to the experimenter’s office to receive their earnings from the experiment.

Note that information in this setting is non-instrumental in the sense that the lottery is an exogenous event which cannot be influenced by the subjects. One might however argue that information has at least some instrumental value as it may allow subjects to improve their decision on whether to stop participating in the experiment or not, i.e., to stop calling or not to pick up their money, depending on their chances of winning the lottery. If this were the case, subjects should have preferred the clumped condition over

11_{Subjects could call from 9am to 12pm and from 2pm to 5:30pm. Alternatively they could show up}

personally in the experimenter’s office which only one subject chose to do.

12_{In treatments 3 and 4, some subjects did not participate in the lottery but received a fixed payment,}

depending on the outcome of the price list format. Nevertheless these subjects still had to call from Tuesday to Thursday and this was made clear in the instructions.

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the piecewise condition, because it provided them with all the information on Tuesday, allowing them to decide on Tuesday whether the revenues from the experiment outweigh the cost of calling and picking up the money. We argue that the minimum payoff from the experiment (15 Euro) is big enough for subjects to continue with the experiment, even if they know they lost in the lottery. This is supported by the low number of subjects who failed to call or to collect their revenues from the experiment and by the fact that these numbers do not differ between treatments.13 _{Furthermore, in case this argument}

were valid, it would only bias our results in favor of Kőszegi and Rabin’s model.14

All experiments were conducted using paper and pencil. A total of 104 subjects participated in the experiment, 24 in treatments 1 and 2 respectively, 30 in treatment 3 and 26 in treatment 4. We ran 2 sessions per treatment. Subjects were students from different fields.

1.2.3

Hypotheses

Here we intuitively derive the predictions of Kőszegi and Rabin (2009). In Appendix A we formally derive the proposition by Kőszegi and Rabin (2009) that individuals prefer information in one piece, and derive predictions for our treatments.

A central assumption in Kőszegi and Rabin (2009) is that utility depends on an-ticipated changes in beliefs about current and future consumption. Beliefs are derived from rational expectations and people are loss averse with regard to changes in their be-liefs. Loss aversion in belief changes implies an aversion towards gradual resolution of uncertainty. Piecewise information exposes people to fluctuations in their beliefs. Since bad news decrease utility more than good news increase it, these expected fluctuations in beliefs do not cancel in utility terms. Consequently people seek to avoid piecewise information.

In addition the model assumes that people care (weakly) less about changes in beliefs, the further away the time of belief change lies from the actual point of consumption. In

13_{In treatment 1, one subject failed to collect its revenues. In treatment 3 one subject failed to call, in}

treatment 4, 2 subjects failed to call.

14_{One might also argue that information in our setting might be instrumental in the sense that early}

information allows subjects to improve their inter-temporal consumption smoothing. We believe that this effect is negligible in our setting, given that consumption smoothing occurs over a whole life-span. Again, if this effect were present, it would only bias our results in favor of Kőszegi and Rabin’s model.

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other words, a person is assumed to be less sensitive to changes in beliefs, the more time lies in between news and the time of consumption. This implies that people (weakly) prefer to receive information sooner rather than later. Note that this assumption also has consequences for the preference for clumped information. When comparing conditions where information is clumped to piecewise information conditions, the time information arrives is necessarily affected. It is impossible to collapse different pieces of information into one piece, without changing the time the pieces of information are received. There-fore, the precise prediction of Kőszegi and Rabin (2009) is that people prefer to receive information clumped rather than piecewise, as long as no information is delayed through clumping.

Therefore, subjects in treatments 1 and 2 should strictly prefer the clumped condition over the piecewise condition and consequently select the clumped condition.

HYPOTHESIS 1: In treatments 1 and 2 subjects choose to receive information in one piece.

Likewise, the model predicts that the average willingness to pay for the lottery should be higher in treatment 3 (where subjects receive clumped information) compared to treat-ment 4 (where subjects receive information piecewise).

HYPOTHESIS 2: Average willingness to pay for the lottery should be higher in treatment 3 compared to treatment 4.

1.3

Results

First, consider treatments 1 and 2, where subjects could directly choose between the two information conditions. Figure 1.2 summarizes results from the two treatments. In treatment 1, only 11 out of 24 subjects preferred to receive information clumped rather than piecewise. In treatment 2, 14 out of 24 preferred the clumped information condition. Comparing choices between treatments 1 and 2, we find no significant difference. Using a Fisher Exact Test we cannot reject the null-hypothesis choices do not differ between the treatments (p-value is 0.56). Using a simple Probit regression, regressing the choice

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between the information conditions on a constant and a treatment dummy delivers similar results. The coefficient of the treatment dummy is not significantly different from zero (p-value =0.39). 0.4 0.5 0.6 0.7 0.8 0.9 1 R el at iv e F re q u en cy Treatment 1 Treatment 2 0 0.1 0.2 0.3 0.4 Clumped Piecewise R el at iv e F re q u en cy

Figure 1.2: Relative frequency of choices (clumped or piecewise information) for treat-ments 1 and 2.

Given that we find no treatment difference, we henceforth analyze pooled data for treatments 1 and 2. 25 out 48 subjects preferred to receive information in one piece. This is clearly inconsistent with Kőszegi and Rabin (2009), which predicts that all subjects should prefer the clumped information condition. However, when evaluating the predictive power of the model with our data, we need to incorporate an error structure that captures possible inconsistencies and mistakes of subjects. Thus, the statistical model we evaluate is one where subjects make a mistake with probability pe. Since the model predicts that all subjects prefer the clumped condition, pe denotes the likelihood that the piecewise condition is chosen. With probability (1− pe) they make no mistake and choose the clumped condition. As a first step we simply assume pe = 0.2, i.e., we evaluate the model allowing for error rates of up to 20 percent. Given that Kőszegi and Rabin (2009) predict a strict preference for clumped information, we believe that an error rate of 0.2 is fairly high. We use a simple Binomial Test to test the null hypothesis that our data are generated by a preference for clumped information and an error rate of 20 percent or lower, i.e., thatpe ≤0.2. We reject the null hypothesis at any conventional level (p-value < 0.00001).

In the next step we ask which error rate we would have to assume such that the data is compatible with the model’s prediction, i.e., such that we cannot reject the null

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hypothesis that people prefer clumped information. More precisely, we ask for which value ofpewe cannot reject the nullyhypothesis (at the 5 percent level) that people prefer clumped information, using a one-sided Binomial Test. We find that this threshold value of pe is 0.354. Thus, we cannot reject the null hypothesis that pe ≤ 0.354 (p-value = 0.0502). We conclude that our data is only compatible with the prediction of Kőszegi and Rabin (2009), if we are willing to assume that subjects make mistakes with a probability of more than 35 percent.

It might be that people are heterogenous in their attitudes towards different resolutions of uncertainty. Thus one could ask which individual characteristics determine preferences towards the resolution of uncertainty. Obvious candidate is our measure of loss aversion. The aversion to piecewise information in Kőszegi and Rabin (2009) is driven by loss aver-sion in belief changes. Thus, it could be that more loss averse subjects have a preference for clumped information. We split our sample according to a high or low degree of loss aversion.15 For subjects with a low degree of loss aversion, 57.14 percent preferred the clumped condition over the piecewise condition. For subjects with a high degree of loss aversion, exactly 50 percent preferred to receive information clumped. Thus we do not find that subjects with a high degree of loss aversion prefer the clumped condition more frequently.

We summarize our findings from treatments 1 and 2 as follows:

RESULT 1: Putting treatments 1 and 2 together, only 25 out of 48 subjects preferred the clumped information condition. We can reject the hypothesis that people prefer clumped over piecewise information, even if we allow for error rates of 20 percent. Our results are only compatible with a preference for clumped information if we are willing to assume error rates of more than 35 percent.

Next, consider behavior in treatments 3 and 4. Average willingness to pay for the lottery is 25.93 Euro and is below the expected value of the lottery of about 32 Euro. Figure 1.3 shows a histogram of subjects’ willingness to pay for the lottery for both

treat-15_{Recall that we used two lottery choices to elicit a measure of loss aversion. We classify subjects who}

reject both gambles as having a high degree of loss aversion. Subjects who accept both gambles or reject the gamble in choice 1 and accept the gamble from choice 2 are classified as having a low degree of loss aversion. Note that a total of 5 subjects did not behave consistently in the two loss aversion choices. Inconsistency means that they reject the gamble from choice 2 but accept the gamble from choice 1.

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ments. Kőszegi and Rabin (2009) predict that subjects should have a higher willingness to pay in treatment 3, where information was clumped. However, Figure 1.3 suggests the opposite. While about 37 percent of subjects in the clumped condition (treatment 3) report a willingness to pay of 23 Euro or lower, only about 27 percent do so in the piecewise condition (treatment 4). On the other hand, while about 27 percent in the piecewise condition report a willingness to pay of 32 Euro or higher, the fraction is only 3 percent in the clumped condition. The average willingness to pay is 24.83 in treatment 3 compared to 27.19 in treatment 4. Using an OLS regression, regressing willingness to pay for the lottery on a constant and a treatment dummy, we can reject the null hypothesis that willingness to pay is higher in the clumped information condition (p-value<0.05).16

This result is robust when controlling for our measure of risk aversion or gender.17

0.15 0.2 0.25 0.3 0.35 R el at iv e F re q u en cy Treatment 3 Treatment 4 0 0.05 0.1 [<20] [20-23] [24-27] [28-31] [32-35] [>35] R el at iv e F re q u en cy

Willingness to Pay for Lottery

Figure 1.3: Relative frequency of willingness to pay for lottery for treatment 3 (clumped information) and treatment 4 (piecewise information).

Now consider our measure of loss aversion. Again, we split our sample according to high and low degree of loss aversion.18 For subjects with a low degree of loss aversion,

16_{Kőszegi and Rabin (2009) provide a directed null hypothesis to test. Consequently we use one-sided}

test statistics to test their predictions.

17_{Note that out of the 56 subjects, 3 failed to make consistent choices in the multiple price list format.}

In the analysis above we used their average switching point in the price list format. Our results are robust when using the first switching point instead, or excluding them from the sample. When using the first switching point for these three subjects, average willingness to pay for the lottery is 24.17 in treatment 3 and 26.69 in treatment 4. Regressing willingness to pay for the lottery on a constant and a treatment dummy, we can still reject the null hypothesis that willingness to pay is higher in the clumped information condition (p-value <0.05). When we exclude the three inconsistent subjects from the sample, average willingness to pay for the lottery is 24.85 in treatment 3 and 27.16 in treatment 4. Regressing willingness to pay for the lottery on a constant and a treatment dummy, we again reject the null hypothesis that willingness to pay is higher in the clumped information condition (p-value=0.06).

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average willingness to pay is 25.64 in the clumped information treatment and 28.38 in piecewise information treatment. For subjects with a high degree of loss aversion, this difference is smaller. Average willingness to pay is 24.42 in the clumped condition and 24.44 in the piecewise condition. The smaller treatment difference is somewhat in line with Kőszegi and Rabin (2009). Note however that also for subjects with a high degree of loss aversion, average willingness to pay is not higher in the clumped information con-dition.

RESULT 2: The average willingness to pay for the lottery is higher in treatment 4 compared to treatment 3. We reject the null hypothesis that subjects have a higher willingness for the lottery when information is clumped.

1.4

Conclusion

We examined individuals’ attitudes towards information regarding exogenous events. While “standard” theory predicts indifference between different types of resolutions of uncertainty, other theories propose that people care about the timing of information. In this chapter we used a controlled lab experiment to test a prediction developed in Kőszegi and Rabin (2009) that people prefer to receive information in one piece rather than piece-wise. Our experimental data does not support the hypothesis that piecewise information is utility-decreasing. In the following we discuss several possible explanations.

First, there is a general problem of testing dynamic models of decision making as these models usually do not specify the length of a time period. In principle time periods could be seconds, minutes, days or months. From a theoretical perspective this makes perfect sense. In fact it seems impossible to determine exact specifications as these are likely to depend on various factors, e.g, the context of the decision-problem. From an empirical perspective this is challenging. It could be that failure to support Kőszegi and Rabin (2009) is due to failure to create timing structures that affect different time periods. Note, however, that in our experiment we made a high effort to make variations in the timing structure meaningful by running the experiment over days. Note also that while leaving the length of a time period open, Kőszegi and Rabin (2009) also do not exclude any specifications.

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Second, while we did not find support for the hypothesis on an aggregate level, it might be that some subjects do have preferences for receiving information in one piece. People might be heterogenous in their preferences for different information structures and it would be interesting to analyze which individual characteristics determine these preferences. Note, however, that our data on individual degree of loss aversion does not deliver a subgroup that shows a clear preference for information in one piece.

Third, the prediction that piecewise information is utility decreasing might only hold in certain decision environments. The model by Kőszegi and Rabin (2009) requires people to anticipate utility consequences of future belief changes and incorporate them in their current choices. These anticipation effects might only be present in contexts of particular significance, e.g., news about the own health condition or that of close relatives, news about the future career or maybe news about important political events. Note, however, that expected payoffs and payoff differences between winning and losing of the lotteries in our experiment are rather large. In one treatment, the payoff difference between winning and losing was 500 Euro, which is probably more than half of the monthly income of an average student in our sample.

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Chapter 2

Image and Misreporting

2.1

Introduction

Individuals hold private beliefs about their performance, skills, abilities and achievements. Transmission of this private information is crucial for the efficiency of economic interac-tions. For instance, efficient allocation of tasks within a firm relies on information about employees’ skills and abilities. The same is true for decisions about job promotions or efficient specialization. In insurance contexts, the design of efficient insurance plans is difficult when individuals hold private information about their underlying risk. In this chapter, we analyze whether individuals’ image concerns can lead them to misreport pri-vate information in situations, where from a traditional, purely pecuniary perspective, truthful revelation would be optimal. Individuals that care about how they are perceived by their environment, will take this perception into account when making choices or as-sessing own performance and abilities in front of others. We illustrate with a simple model how image concerns make people misreport their own performance, skill or abil-ity. In equilibrium, some individuals with low performance will choose to report high performance. Consequently, reports become less informative. Then we provide evidence from a lab experiment documenting the consequences of a desire for a favorable image on statements about own performance.

In our model, decision makers’ choice is to publicly report private information about their own type. Correctly stating their private information is optimal in direct monetary terms. However, we assume that decision makers’ utility consists of two components, a “standard” part, reflecting direct monetary concerns and an image part, reflecting

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rep-utational concerns. The way we model image concerns is a shortcut that captures all potential benefits from signaling a high type. The nature of reputational concerns could be strategic. In labor market contexts, signaling of abilities and skills may improve hiring prospects and lead to higher wages or promotion. Benefits could also be in the form of social approval. Alternatively, decision makers could value reputation for hedonic reasons. People simply enjoy being regarded as a high type. We show the existence of a unique Perfect Bayesian Nash equilibrium, where a decision maker misreports private informa-tion. Low skilled types choose to signal a high type, if image concerns are relevant. We also show that misreporting increases in the relative importance of image utility. Apart from sending positive signals about skills and abilities, our model also captures situations where decision makers might want to appear humble or modest in front of others. If mod-esty is the dominant signaling motive, misreporting might go in the opposite direction, i.e., decision makers downplay own skills and display underconfidence. While we focus on social image concerns, our model is also compatible with a self-signaling interpretation where decision makers learn about their own type by inference from own choices (e.g., as in Bénabou and Tirole (2004) and (2006)).

We test the main prediction of our model, that image concerns lead to misreporting of private information, in a laboratory experiment. The experiment has two stages. In stage 1, subjects go through a series of general knowledge quiz questions. In stage 2, subjects are asked to give a binary and incentivized self-assessment concerning their quiz performance. We study two main treatments: In the audience treatment, we exogenously increase subjects’ image concerns in stage 2 by making them report their self-assessment to the other subjects present in the lab. After all subjects have given their binary assessment, one after the other has to stand up and report his or her self-assessment to the group. This procedure has been used by Ariely et al. (2009) to increase image concerns in the context of prosocial decision making. In the private treatment, subjects do not report their assessment to the group. Our data reveals significant evidence for image effects. In the audience treatment, stated self-assessments are significantly higher than in the private treatment. We also document a gender difference in stated self-assessments. This difference seems to be driven by a stronger response of men to the presence of an audience.

To further assess if subjects’ reports are also affected by a desire to appear modest in front of others, we conduct a feedback treatment. The treatment is identical to our audi-ence treatment. The only differaudi-ence is that after subjects report their self-assessments to

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the group, the experimenter will also report the true performances to the group. If misre-porting in the audience treatment was solely driven by the signaling of skills or ability, we should observe that reported self-assessments do not differ between the private and the feedback treatment, because in the latter, true performances will be revealed. If concerns to appear modest are relevant, we should observe stated self-assessments in the feedback treatment below the level we found in the private treatment. When comparing stated self-assessments between the feedback and private treatment, we find no evidence for modesty concerns on the aggregate level. However, we do find some evidence that subjects with rather low quiz performance want to appear modest in the feedback treatment.

Our findings show that image concerns play an important role in the transmission of private information about skill, ability or performance. Even if truthful reporting is optimal in monetary terms, decision makers misreport. This contributes to a large literature that has documented significant biases in stated self-assessments. If individuals are asked to assess their own type in terms of performance or ability, their self-assessments are frequently overly optimistic. One of the most prominent examples of highly optimistic beliefs is a study by Svenson (1981) on relative self-assessments in the context of car driving skills. He finds, for instance, that 40% of subjects place themselves in the top 20% of car drivers with regard to driving skills.1 _{Our theoretical and experimental results}

suggest, that documented biases in self-assessments might be produced by a desire to gain a favorable image. By trying to signal a high type, decision makers appear overconfident. This can occur even with perfect knowledge about their own performance, skill or ability. Decision makers can appear overconfident without any inherent biases in self-assessments. Thus, in our approach, overconfident behavior is rather the outcome of a preference, e.g. a desire to signal skills or ability, than a mistaken self-perception. This might explain why people do not “learn” about their overconfidence over time.

Our findings are also relevant from a mechanism design perspective. They show that mechanisms designed with a purely monetary focus do not necessarily lead to truthful revelation of private information. If people have strong image concerns, these ought to be taken into account when designing optimal mechanisms, e.g., insurance plans or

employ-1_{Other empirical studies on overconfidence include for example Camerer ad Lovallo (1999) and Hoelzl}

and Rustichini (2005). For a recent overview, see Benoit and Dubra (forthcoming). Several studies examine the consequences of overconfidence for behavior in different contexts. Examples are Dohmen and Falk (2011) in the context of tournament entry, Malmendier and Tate (2008) for CEO behavior or DellaVigna and Malmendier (2006) for overestimation of future gym attendance.

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ment contracts. Likewise, our findings are informative from a methodological perspective. They suggest that appropriate monetary incentives alone might not be sufficient to ensure truthful revelation of self-assessments in experiments or surveys. The presence of image concerns creates a trade-off between image concerns and monetary outcomes which leads to biases in stated self-assessments. Minimization of image concerns via, for instance double-blind procedures, might provide a solution to this problem.

While our focus is on direct transmission of private information, our results apply more generally. In many decision contexts that require prior self-assessment, decision makers’ choices allow them to signal skill, ability or performance to others. Consider the choice to enter a tournament. The decision to enter or not clearly depends on individuals’ private self-assessment. The money-maximizing choice for individuals with low skills and abilities is usually not to enter the tournament. In the presence of image concerns, however, individuals with low skills might yet decide to enter, as this allows them to signal skill and abilities to others. In the context of participation in welfare programs, image concerns and social approval seeking might lead to low participation rates due to fear of reputation losses. Moffitt (1983) presents data from different welfare programs in the U.S. in the 1970’s. He reports that as much as 30 - 60 % of the citizens who are eligible for welfare do not apply and argues that this is a consequence of the fear of stigmatization of welfare recipients.

This chapter relates to a few recent papers that considered the social signaling com-ponent of biases in self-assessments. Burks et al. (2010) compare different explanations for overconfidence in a large survey study with truck drivers. Their results suggest a strong connection between image concerns and overconfidence. Truckers reporting that they care about how others perceive them, significantly overplace their performance in an IQ test and a numeracy task. Charness et al. (2011) provide experimental evidence that men exploit the possibility to send an exaggerated productivity signal in a strategic interaction of a tournament entry to deter entry of other individuals while women do not. In their paper, they also find evidence for a consumption value from overconfidence.2 _or

Moebius et al. (2011)). In a related experiment, Reuben and Rey-Biel (2010) find that

2_{Eil and Rao (2011) and Moebius et al. (2011) also provide evidence for a consumption value from}

overconfidence. Bénabou and Tirole (2002) provide a theoretical argument for a value of overconfidence as it can increase motivation of individuals with imperfect willpower. Other models have assumed a value of self-confidence and show how overconfident self-assessments can be produced by selectively choosing information or by asymmetrically processing information (see Brunnermeier and Parker (2005), Kőszegi (2006)

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subjects exaggerate past performance in order to become a group leader.

More broadly, this chapter relates to several papers that study consequences of image concerns on economic decision making in different contexts. So far the literature has mainly analyzed effects of social approval for prosocial decision making. Non-anonymity or the presence of an audience has been shown to increase prosociality (see Gächter and Fehr (1999), Rege and Telle (2004), Andreoni and Petrie (2004) and Ariely et al. (2009)). Theoretical papers analyzing image concerns in a prosocial context include Bénabou and Tirole (2006), Ellingsen and Johannesson (2008) and Andreoni and Bernheim (2009). Closest to our modeling approach is the paper by Bénabou and Tirole (2006). They show how extrinsic incentives can crowd out prosocial behavior, because they destroy the image rewards from prosocial activity.

The remainder of this chapter is organized as follows. The next section introduces our model. Section 2.3 presents the experimental design, section 2.4 the results from our experiment and section 2.5 concludes.

2.2

The Model

We provide a simple framework that allows illustrating how image concerns can influence reports of private information. The next two sections introduce the model, assuming that decision makers have perfect knowledge about their performance. In section 2.2.3 we relax the assumption of perfect knowledge. In section 2.2.4 we show how a desire to appear modest could be captured with our model framework.

2.2.1

Set-Up

Consider decision makers D that differ in a parameter p which is an element of P =

{0,1, ...,p¯}. Depending on the context, p captures D’s ability, skill, performance or achievement. p is D’s private information but is commonly known to be distributed according to a probability function f defined over P. At first, we assume that decision makers have perfect knowledge about p. In section 2.2.3 we provide a version of the model where decision makers have imperfect knowledge about their type and show that this produces qualitatively the same results. Decision makers choice x is to report some measure related to p in public. We assume a binary report: is p larger than some value

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r? This report could be absolute (is phigher than a certain number?), or relative to oth-ers (is p higher than the average or the median performance of other decision makers?). Thus, we have that x ∈ {Y es, N o}. Decision makers win a monetary prize y if their stated report is correct, otherwise they earn 0. Thus, choicexand prize yreflect contexts where truthful reporting of private information is optimal in direct monetary terms. In experimental settings, choicexand prizeysimply capture an incentivized self-assessment. More generally, choice x could be a decision that depends on p, e.g., the choice to enter a tournament, and the prize y reflects direct monetary consequences from that choice. Note that the prize y might also capture direct non-monetary utility consequences from misreporting, e.g, costs of lying.3

We assume that utility has two sources, direct (monetary) payoffs and image util-ity. Money enters linearly in the utility function and the two components are additively separable. Thus utility is given by

U(x) =y1(x) +αβE(p|x).

The first part captures direct utility over money. 1(x) is an indicator function taking the value 1 if the stated report is correct and 0 otherwise. The second part incorporates image utility. E(p|x)is the public’s expectation aboutD’s performance, skill or abilityp, conditional on D’s choicex. Thus, the public infers decision makers’ pfrom their reports, and social approval depends on that. α and β specify the strength of image concerns. α is an individual parameter, i.e., decision makers differ in α. Some D care more about their image or respond more strongly to social approval than others. α is assumed to be constant across contexts and environments. While α is D’s private knowledge, it is commonly known to be drawn from a distribution described by a density function g over [0, α] with g(α)>0, ∀α∈[0, α]. We assume that performance or ability pand the desire for social approvalαare drawn independently. βinstead, is identical for all decision makers and we assume β > 0. β might depend on the context of the decision problem, e.g., the size of the public, the social distance between D and the public or the strategic value of a favorable image. Thus, β is the parameter that is exogenously manipulated

3_{Gneezy (2005) and Fischbacher and Heusi (2008) examine lying behavior in different contexts. They}

find evidence that subjects lie, but also that there is some cost of lying that prevents subjects from lying 100%. Note that throughout the chapter we focus on direct monetary utility, but always mean to include non-monetary interpretations such as costs of lying.

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in our experiment. An alternative interpretation of decision makers’ image concerns is a desire for a positive self-image (similar as in Bénabou and Tirole (2004) and (2006)).4 _In

this case, decision makers receive a private signal about their performance or ability prior to their decision. Thus, when deciding, they hold information about their p. However, for their later self-evaluation, this knowledge is not available for example due to reasons of imperfect recall. Since actions are easier to recall than signals, decision makers base their self-evaluation on past stated reports.

2.2.2

Equilibrium

We now show under which conditions there exists a unique Perfect Bayesian Equilib-rium where decision-makers misreport their private information. In the absence of image concerns, D’s behavior would be straightforward. Decision makers choose x = Y es, if their performance, skill or ability p is higher than r and x =N o otherwise. In the pres-ence of image concerns however, there exists a trade-off between stating a truthful report and gaining social approval. In equilibrium, all decision makers with p > r will choose x = Y es. For decision makers with p < r there exists a threshold type α∗ such that all D with α > α∗ will choose x =Y es and all D with α < α∗ will choose x =N o. This is stated formally in the following Proposition:

PROPOSITION 1: If α is sufficiently large, i.e.,

αβhP p>r f(p)p P p>rf(p)− P p≤r f(p)p P p≤rf(p) i

> y, there exists a unique Perfect Bayesian Equilibrium where decision makers with p < r and α > α∗ choose x=Y es. Decision makers with p > r choosex=Y esand those with p < r and α < α∗ choose x=N o.

Next, we verify that behavior described above is indeed an equilibrium and show that if α(the highest possible realization ofα) is sufficiently large, such an equilibrium always exists. In Appendix B we show that this equilibrium is unique.

First, we state precisely what we mean by α being sufficiently large. We assume that there exist decision makers with image concerns large enough, such that they choose

x = Y es if p < r and all other decision makers simply maximize monetary outcomes.

4_{In the psychology literature, the idea that people construct their self-image from past actions can be}

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More precisely, α is large enough, such that the image gains from choosing x = Y es, αβhP p>r f(p)p P p>rf(p) −P p≤r f(p)p P p≤rf(p) i

, outweigh the monetary costs y.

In equilibrium, all D with p > r choose x = Y es. It is straightforward to show that this is optimal, given that it maximizes both monetary outcomes and image utility. For decision makers with p < r, behavior depends on the strength of image concerns. There exists a threshold type α∗, such that all D with p < r and α > α∗ will choose x = Y es and those with p < r andα < α∗ choosex=N o. The threshold type α∗ with p < r must be indifferent between potential image gains from choosing x=Y esand monetary losses from reporting incorrectly. We have the following indifference condition:

α∗βhP p>rf(p)p+ ´α α∗g(z)dz P p≤rf(p)p i 1 P p>rf(p)+ ´α α∗g(z)dz P p≤rf(p) =y+α∗βP p≤r f(p)p P p≤rf(p).(2.1)

The left hand side captures image utility in case D chooses x=Y es, which is simply a weighted average of the average performance, skill or ability of decision makers with p > r and those with p < r, with weights depending on how many Ds misreport. The right hand side captures image utility when choosingx=N o, which is simply the average performance or ability of Ds with p < r plus the prize y for reporting correctly. Rear-ranging equation 1 leads the following:

α∗β 1 P p>rf(p)+ ´α α∗g(z)dzPp≤rf(p) P p>rf(p)p+ ´α α∗g(z)dz P p≤rf(p)p −P p≤r f(p)p P p≤rf(p) =y.(2.2)

One can see from equation (2) that decision makers withα < α∗ and p < r optimally choose x = N o. As the expression in square brackets (gains in reputation) remains unchanged, but the strength of image concerns is smaller (αβ < α∗β), image gains in total weigh less in utility terms than monetary losses, i.e., they will state a truthful report x = N o. Ds with α > α∗ instead optimally choose x = Y es as their image gains loom larger than their monetary losses. Note also, that if α is sufficiently large, the threshold type α∗ and thus the equilibrium, always exists. To see this, take the left hand side of equation (2) and varyα∗. Ifα∗approaches zero, the left hand side approaches zero as well. As α∗ approaches α, the left hand exceeds y by assumption. Furthermore, the left hand side is continuous and strictly increasing in α∗. Consequently, there necessarily exists an α∗ for which equation (2) holds.

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PROPOSITION 2: An increase in β reduces the threshold typeα∗. Consequently, more decision makers with p < r misreport by choosing x=Y es.

Proposition 2 shows how reports change inβ, for example, when the size of the public, the social distance betweenDand the public, or the strategic value of reputation changes. Considering equation (2), one can see that a change inβaffects the threshold typeα∗. An increase in β reduces the threshold type, in other words, more decision makers withp < r will choose x=Y es. Thus, our model predicts that an exogenous increase in image con-cerns increases the number of decision makers that misreport information. Consequently, reports become less informative.

2.2.3

Model with Imperfect Knowledge

So far, we assumed that decision makers perfectly know theirp. However, one could argue that in most real-life situations, individuals only have imperfect knowledge about their skills or abilities. Also, in our experiment subjects are likely to be uncertain about their performance. In this section, we analyze what happens if decision makers have imperfect knowledge about their type but know more than the public. The crucial difference to the case with perfect knowledge is that type-uncertainty weakens the informativeness of decision makers choices. Intuitively, it is more difficult for the public to infer ability from choices, if decision makers themselves are uncertain about their ability.

The set-up is identical to above. The only difference is that decision makers do not perfectly know their p. Instead, they hold a point belief pˆ∈ {0,1, ...,p¯} and pˆis (poten-tially) different from p.5 _{D’s choice} _x _{is again to report whether} _p _{is larger than some}

valuer, i.e.,x∈ {Y es, N o}. Given their imperfect knowledge aboutp, it is possible that decision makers wrongly assess whether their p is larger or smaller than r. We specify¯

the imperfect knowledge about p as follows. Letφ(p) denote the likelihood that decision makers point belief pˆ is larger (smaller) than r¯ although the true p is smaller (larger). Thusφ(p)is the probability thatp >ˆ r¯althoughp <r¯orp <ˆ r¯althoughp >r. We make¯

the following assumptions about φ(p). First of all, we naturally assume that φ(p) < 1₂ for all p. Second, we assume that φ(p) is strictly increasing in p for p < r, and strictly¯

decreasing in p for p > r. In other words, the likelihood that¯ Ds think that their p is

5_{To focus on the effect of type uncertainty on the informativeness of choices, we abstract from risk by}

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larger (smaller) thanr, although it is smaller (larger) increases the smaller the difference¯

betweenpandr. Intuitively, the binary self-assessment should be easier, the further away actual performance is fromr and consequently, the frequency of mistakes should be lower.

We now s

Essays in Behavioral Economics